A near total lack of combat training? Immortality doesn't mean a thing if you'll just keep getting shot and cut up. Not to mention he may figure out if a bullet to the back of the brain kills Sylar, it'll work on Claire too. Or, just discover it by accident.
Actually, Claire knows that they know how to kill her.
There was the whole scene where the guy grabbed her and said he was going to put her down by shooting her right in the back of the head. That's when HRG came in and Claire was horrified/scared that "they were really going to pull the trigger" and HRG confirmed that they have no qualms about killing you. So, in my mind, Claire was doing what she could to provide distraction, but at the same time, perhaps for the first time that she control of her powers can she actually still feel "mortal" and in danger from them since they know her 'kill spot'